Nuclear halo of a 177 MeV proton beam in water: theory, measurement and parameterization

The dose distribution of a monoenergetic pencil beam in water consists of an electromagnetic "core", a "halo" from charged nuclear secondaries, and a much larger "aura" from neutral secondaries. These regions overlap, but each has distinct spatial characteristics. We have measured the core/halo using a 177MeV test beam offset in a water tank. The beam monitor was a fluence calibrated plane parallel ionization chamber (IC) and the field chamber, a dose calibrated Exradin T1, so the dose measurements are absolute (MeV/g/p). We performed depth-dose scans at ten displacements from the beam axis ranging from 0 to 10cm. The dose spans five orders of magnitude, and the transition from halo to aura is clearly visible. We have performed model-dependent (MD) and model-independent (MI) fits to the data. The MD fit separates the dose into core, elastic/inelastic nuclear, nonelastic nuclear and aura terms, and achieves a global rms measurement/fit ratio of 15%. The MI fit uses cubic splines and the same ratio is 9%. We review the literature, in particular the use of Pedroni's parametrization of the core/halo. Several papers improve on his Gaussian transverse distribution of the halo, but all retain his T(w), the radial integral of the depth-dose multiplying both the core and halo terms and motivating measurements with large "Bragg peak chambers" (BPCs). We argue that this use of T(w), which by its definition includes energy deposition by nuclear secondaries, is incorrect. T(w) should be replaced in the core term, and in at least part of the halo, by a purely electromagnetic mass stopping power. BPC measurements are unnecessary, and irrelevant to parameterizing the pencil beam.